writing equations using variables that are functions of eachother.

Question

Use lower case letters in your answers to the following:

(a) Express the area of a circle, A, as a function of its circumference, c.
A(c) = 

(b) Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/8 of the height.
V(r) = 

(c) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 6 square feet.
D(w) = 

I usually can attempt to give an answer but I have no idea how to do this one. Could you please explain the answer and how to get there.

Answer 1

I will give you some help below.     

(a) Express the area of a circle, A, as a function of its circumference, c.
A(c) =

c = 2(pi)r so r = c/[2pi]  Forgive me for using pi--the character available does not look good on this Website

so A(c) = pi•[c/(2pi)]² and I am going to let you simplify this!

(b) Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/8 of the height.   
V(r) = (1/3)(pi)r²h   but you'll substitute for r: r = h/8   and then simplify!

(c) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 6 square feet.
D(w) =    

A = 6 = Lw so L = 6/w  & thus the diagonal is the hypotenuse of a rt triangle with legs w and 6/w.  Now substitute & simplify.